General Equilibrium ICE-Table Solver implementation

Binding contract

This record describes what an executable surface must bind and validate. It does not claim that a public calculator, package, or production route is deployed.

Record owner

Guth Instruments

Lifecycle

verified-with-binding-errata

Evidence ID

t8-009

Effect

Computation or source lookup only

Input and validation requirements

A naive Newton-Raphson implementation initialized at x=0 encounters K=[B]/[A]^2=1/0 for the 2A ⇌ B trap, producing an undefined function value before it can iterate. The solver also must explicitly reject algebraic roots that produce negative concentrations and must expose the extent-direction convention.

Required corrections

[
  {
    "vector": 4,
    "field": "extent_x / equilibrium_concentrations",
    "wrong": "x=-0.8, [A]=0.8, [B]=0.2",
    "correct": "x=-0.2, [A]=0.2, [B]=0.8",
    "cause": "own working solves 1=-5x => x=-0.2 and states '[A]eq=0-(-0.2)=0.2' and '[B]eq=1-0.2=0.8' explicitly, then the field ships x=-0.8 with concentrations swapped"
  }
]

Inspectable interface fixture

The sample below is evidence for interface and validation tests, not a production implementation.

{
  "inputs": {
    "balanced_equation": "A ⇌ B",
    "initial_concentrations": {
      "A": "1.0000000 M",
      "B": "0.0000000 M"
    },
    "Kc": 4
  },
  "expected_outputs": {
    "K_expression": "Kc = [B]/[A] = x/(1-x)",
    "extent_x": "0.80000000 M",
    "equilibrium_concentrations": {
      "A": "0.20000000 M",
      "B": "0.80000000 M"
    },
    "ice_table": {
      "A": {
        "initial": "1.00000000 M",
        "change": "-0.80000000 M",
        "equilibrium": "0.20000000 M"
      },
      "B": {
        "initial": "0.00000000 M",
        "change": "+0.80000000 M",
        "equilibrium": "0.80000000 M"
      }
    },
    "mass_action_check": "0.80000000/0.20000000 = 4.0000000"
  },
  "reference_data": {
    "method": "Solve x/(1-x)=4 within 0 <= x <= 1."
  },
  "working": "Initial: A=1, B=0. Change for A ⇌ B: A decreases by x and B increases by x. Therefore [A]eq=1-x and [B]eq=x. Set Kc=4: x/(1-x)=4. Multiply through: x=4-4x. Add 4x: 5x=4. Divide by 5: x=0.80000000 M. Then [A]eq=1-0.8=0.20000000 M and [B]eq=0+0.8=0.80000000 M. Check: 0.80000000/0.20000000=4.0000000."
}

Other records

Sources and evidence

These pointers bind the page to evidence. They do not grant authority or collapse verification into deployment.

• VERIFIED_LEDGER.json
• evidence-tranche8/tranche8-results.json
• tranche errata record